Probability mapping system

ABSTRACT

A processor-based system for generating a probability map may include at least one processor. The at least one processor may be configured to receive data associated with a quantity to be mapped and apply a processor-based mapping algorithm to generate a first map of values for the quantity within an area of interest. The processor may also be configured to modify at least one or more of data provided as input to the mapping algorithm or one or more input parameters associated with the mapping algorithm and generate at least a second map of values for the quantity within the area of interest; and generate a probability map associated with the quantity based on the first and second maps.

TECHNICAL FIELD

The presently disclosed embodiments relate generally to systems andmethods for generating data maps. More specifically, the presentlydisclosed embodiments may include systems and methods for quantitativelygenerating probability maps relating to quantities in an area ofinterest.

BACKGROUND

Many industries have an interest in mapping values for a particularquantity over an area of interest. Such maps may aid in performing tasksassociated with the industry. For example, maps showing water depths areimportant in maritime shipping and navigation. Contour maps showing landelevations may be used in planning communities, building roads,constructing reservoirs, etc. In the oil and gas exploration industry,maps showing the locations of oil deposits can help in deciding whereand whether to initiate a drilling project. Maps of soil contaminationlevels can be used in clean up or treatment efforts.

The accuracy of such maps over an area of interest can be crucial. Forexample, in the oil and gas exploration industry, reliance on a mapinaccurately suggesting the presence of oil and gas deposits may havesignificant negative consequences. All costs associated with equipment,personnel, and operations would be lost if drilling operations wereestablished at a location mapped as having high oil concentration levelsonly to later discover through drilling that little oil was present atthat location. Similar economic consequences may be realized in otherindustries that depend on mapped data.

In certain situations, creating accurate maps can be challenging. Forsome quantities, such as elevation, temperature, etc., measurement ofparticular values over an entire area of interest may be readilyascertainable using scanning measurement equipment to generate contourmaps. Even in these situations, however, obtaining a desired level ofprecision in the measured data and in the coverage of data over the areaof interest may be complex. In other cases, it may be difficult orimpossible with known techniques to obtain a data scan over an entirearea of interest. For example, oil or gas deposits may reside withinstone layers or formations located deep below the Earth's surface.Determining the thickness of these stone layers may require drilling inseveral finite locations to determine the particular thickness valuesfor the stone layer at those locations. Often it may be possible orpractical to obtain measurements at a relatively small number of samplesites within an area of interest. As a result, data relating to aparticular quantity of interest may be available for only a finitenumber of sample locations within the area of interest.

Generating a contour map of a particular quantity over an area ofinterest requires data corresponding to the values for that quantityover the area of interest. Where measured data is available for only afinite set of locations within the area of interest, a process of dataextrapolation or projection is required to obtain calculated (estimated)data values to fill in the gaps between locations corresponding to themeasured values. Various gridding techniques and extrapolation orestimation algorithms may be employed to calculate data values tosupplement measured data within an area of interest. Often, suchtechniques involve averaging techniques to calculate predicted datavalues in the areas surrounding the measured values.

In addition to contour maps showing the measured and predicted datavalues over an area of interest, similar maps may be generated to mapprobabilities associated with the measured and predicted data values.For example, such probability maps may provide contours of percentages.In some cases, the percentages may be indicative of the likelihood thata particular quantity exceeds a certain value within the area ofinterest. Returning to the oil and gas example, a probability map mayindicate over the area of interest the probability that a sub-surfaceoil-containing formation has a thickness greater than a predeterminedvalue (e.g., 10 feet or any other thickness of interest).

While such probability maps can be useful in decision making (e.g.,deciding where and whether to establish an oil or gas drillingoperation), the current methods of generating such probability maps haveseveral drawbacks that can lead to probability maps that have muchhigher levels of uncertainty than the mapped probabilities suggest. Forexample, any single map (or grid) generated using a specific griddingalgorithm and a specific set of input parameters may look different(sometimes substantially different) from other maps generated witheither different algorithms and/or different input parameters. Otherthan empirical measurement for all points on the map, there is no way todetermine which of the generated maps is correct. In fact, none of thegenerated maps is likely correct, as each merely represents a singlepossibility. Only by generating a statistically significant number ofmaps with a statistically reasonable range of parameters can one arriveat a statistically valid interpolation between known data points.

Second, many known techniques for generating probability and statisticalmaps are based on locally calculated statistics which are then mapped.To the extent that many (if not all) gridding and mapping algorithmsconstitute some form of averaging tool, such an approach can bemathematically flawed, as average probabilities generated from averagedvalues would involve taking an average of a set of averages and/or astandard deviation of a set of standard deviations. There is a need formethods and systems for generating more robust probability maps.

SUMMARY

A processor-based system for generating a probability map may include atleast one processor. The at least one processor may be configured toreceive data associated with a quantity to be mapped and apply aprocessor-based mapping algorithm to generate a first map of values forthe quantity within an area of interest. The processor may also beconfigured to modify at least one or more of data provided as input tothe mapping algorithm or one or more input parameters associated withthe mapping algorithm and generate at least a second map of values forthe quantity within the area of interest; and generate a probability mapassociated with the quantity based on the first and second maps.

A computer readable storage medium having computer readable program codeembodied in the medium for use by a processor-based system in generatinga probability map may include program code configured to receive dataassociated with a quantity to be mapped. The program code may also beconfigured to apply a processor-based mapping algorithm to generate afirst map of values for the quantity within an area of interest; modifyat least one or more of data provided as input to the mapping algorithmor one or more input parameters associated with the mapping algorithmand generate at least a second map of values for the quantity within thearea of interest; and generate a probability map associated with thequantity based on the first and second maps.

A method of generating a probability map may include receiving dataassociated with a quantity to be mapped and applying a processor-basedmapping algorithm to generate a first map of values for the quantitywithin an area of interest. The method may also include modifying atleast one or more of data provided as input to the mapping algorithm orone or more input parameter associated with the mapping algorithm andgenerating at least a second map of values for the quantity within thearea of interest; and generating a probability map associated with thequantity based on the first and second maps.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagrammatic representation of devices and systems that maybe used to implement the probability mapping system and method,according to the exemplary disclosed embodiments.

FIG. 2 provides an example set of input data for a quantity to be mappedover an area of interest.

FIG. 3 provides an exemplary map of quantity values over an area ofinterest.

FIG. 4 provides an exemplary map of quantity values over an area ofinterest.

FIG. 5 provides an exemplary map of quantity values over an area ofinterest.

FIG. 6 provides an exemplary binary map of quantity values over an areaof interest.

FIG. 7 provides an exemplary binary map of quantity values over an areaof interest.

FIG. 8 provides an exemplary binary map of quantity values over an areaof interest.

FIG. 9 provides an exemplary probability map generated in accordancewith the exemplary disclosed embodiments.

DETAILED DESCRIPTION

The presently disclosed systems and methods may involve the use ofStochastic/Monte-Carlo techniques in the mapping of discrete spatiallyvarying data or spatially varying probability functions. Using suchtechniques may yield statistically robust probability maps and otherstatistical maps, including, for example, statistical maps of the mean,median, mode, range, deviation, standard deviation, etc. of a quantityover an area of interest. The systems and methods of the presentlydisclosed embodiments may be applicable to the mapping of any data thatcan be displayed in a geographic information system, including but notlimited to geologic, geophysical, reservoir engineering, mining,meteorological, oceanographic, and environmental data, among others.Other data types that may be used may include geographic, topographic,bathometric, petrophysical, atmospheric, hydrologic, pedologic (soil),chemical, sociologic, economic, biologic, zoological, botanical,epidemiologic, political, ecologic, etc. Such data may include, forexample, values associated with quantities such as thickness, elevation,net to gross ratios, porosity, permeability, water saturation,hydrocarbon saturation, mineral percentage, pollution level,contamination level, temperature, depth, salinity, rainfall level, windspeed, humidity, etc. Further, the disclosed techniques are not limitedto two or three dimensional space, but can be expanded to phenomena thatvary over time (four dimensional spaces) or even to conceptualmulti-dimensional spaces.

FIG. 1 provides a diagrammatic illustration of various devices, systems,and components consistent with the presently disclosed embodiments. Forexample, systems and devices that may be configured to generate and/ordisplay the disclosed probability maps may include processor-baseddevices, such as a laptop computer 100, a desktop computer system 110, amainframe server 120, smart phone 130, cell phone 140, tablet computer150, etc. Each may include one or more processors or processing unitsconfigured to perform various operations associated with generation ofthe disclosed probability maps. Such processors may include, forexample, central processing units, digital signal processors,applications processors, embedded processors, or any other logic-baseddevice configured to execute instructions.

Systems for generating the presently disclosed probability maps may becompatible with various operating systems, such as Windows, Mac, Linux,Unix, etc. A probability map generating system consistent with thepresently disclosed embodiments may include any software applications,software components, computing systems, hardware components, etc. thatmay participate in the process of generating a probability map. In somecases, a probability map generating system may include a stand-alonecomputer including probability map generating software. In otherembodiments, the system may include a processor having access toinstructions associated with probability map-generating software.

In still other embodiments, the probability map generating systems mayinclude processors configured to run applications that access featuresprovided by separate probability map-generating code. That is,probability map generating systems may include software, which mayfunction as a stand-alone software package or that may be incorporatedinto other software packages as an “add on” or as an embedded component.For example, software configured to generate the disclosed probabilitymaps may be included with industry standard geographic informationsystem (GIS) mapping packages. In the oil and gas industry, suchpackages may include ArcView, Petrel, Kingdom, Zmap, CPS3, etc. Othersimilar software packages may be used in other industries such asmeteorology, oceanography, geography, environmental sciences, etc.Software configured to generate the disclosed probability maps may alsobe incorporated into or used with generalized packages, such as GoogleEarth and Google Maps.

Any or all examples of such devices may be connected over variousnetworks 160, such as local or wide area networks, the Internet, etc.Various devices may be employed to generate or display the disclosedprobability maps. Such devices may include display screens associatedwith laptop 100, desktop 110, and devices 130, 140, and/or 150. Suchdevices may also include networked of Internet televisions, a printer170, a plotter 180, or any other devices for generating and/ordisplaying mapped probability data.

The presently disclosed systems and methods may generate probabilitymaps based on any suitable input data. In some embodiments, the datainput to the mapping system may include discrete data, which may bedescribed as X, Y, Z, where the X and Y data points provide a geographicreference (e.g., a location within an area of interest), and Zrepresents the parameter under investigation. Such, X and Y terms mayinclude geographic references from a latitude and longitude based systemor from any other suitable cartographic projection system such as, forexample, Universal Transverse Mercator (UTM), U.S. State Plane Systems;international cartographic projections, etc.

In other embodiments, the data input to the probability map generatingsystem may include data in the form of probability distributions. Insuch cases, the input data could be represented either as: (X, Y, T, A,B) or (X, Y, T, A, B, C). Here, the X and Y variables also provide ageographic location within an area of interest, as described above. Ineither case, the “T” value may correspond to an identifier thatspecifies the type of probability distribution. Such probabilitydistribution types may include, for example, normal or Gaussian,exponential or log normal, beta or spline, triangular, rectangular ortrapezoidal, histogram, etc.

The five-term input, (X, Y, T, A, B), may be appropriate for Normal,Gaussian, Log normal and exponential distributions where thedistribution can be described using two terms, A and B, where these twoterms could represent mean and standard deviation, P10 and P90, P1 andP99, P50 and P90, etc. The six-term format, (X, Y, T, A, B, C), may beappropriate for spline, beta and triangular distributions, where the A,B and C terms could represent minimum, mode, and maximum values.Trapezoidal, histogram and other distributions may require morecomplicated input formats.

Whether the input data to the probability mapping system representsdiscrete data or data in the form of probability distributions, theinput data may be known only for certain specific locations within anarea of interest. Away from these certain locations, measured or knowninput data would be unknown.

Various types of discrete data may be used as input to the disclosedprobability mapping system. For example, from the oil and gas industry,discrete input data may include reservoir sandstone thickness, net togross ratios, porosity, permeability, water saturation, hydrocarbonsaturation, mineral concentration or percentages, among others. In theenvironmental industry, discrete input data may include ground watercontamination, contaminant concentration or percentages, leadconcentration, copper concentration, arsenic concentration, hydrocarbonconcentration, mercury concentration, soil contamination, among others.In the field of oceanography, discrete input data may include watertemperature, water salinity, depth, etc. In the field of meteorology,discrete input data may include pollution percentages and types,temperature, rainfall, wind speed, humidity, etc.

Input data in the form of a probability distribution may be similarlyvaried. For example, input data in the form of a probabilitydistribution may be provided to the probability map generating systemfor any of the above examples of discrete input data types where thereare known or assumed errors in the measurement that can be expressed interms of a probability function or where the data points constituteaverages, such as average temperature, average porosity, averagerainfall, etc.

Input data may be provided to the input mapping system by any suitablemethod. For example, input data may be tabulated in predeterminedtemplates stored in memory and accessible to the processing system.Input data may be scanned into electronic form and stored. The inputdata may be provided via a graphical user interface, ASCII flat files,Excel spreadsheets, text files, relational databases, or any othersuitable electronic process or format. Various optical characterrecognition utilities may be used to process or condition the inputdata.

In embodiments where the probability mapping systems includemap-generating software configured to operate in conjunction with othersoftware applications, as an add-on to other software applications,and/or as an embedded feature to other software applications, input datato the probability map generating system or software may be deliveredfully or partially through those other software applications. Forexample, various software-based mapping packages (e.g., ArcView, Petrel,Kingdom, Zmap, CPS3, etc.) include dedicated databases for managingdata. Such databases allow for maintenance and processing of data in amanner especially suited to the mapping packages that use the data. Datacan be optimized, sorted, and quickly delivered to various components ofthe mapping package, as needed. The presently disclosed probabilitymap-generating systems may be configured to leverage and take advantageof preexisting database management facilities of other softwarepackages.

FIG. 2 provides a graphical representation of an example set of inputdata 200 for a quantity to be mapped over an area of interest. In thisexample, input data 200 may be represented in the X, Y, Z format. The Xand Z parameters provide a geographic reference point, such as a spatiallocation within an area of interest. The Z parameter associates ameasured value for a quantity with the geographic reference pointspecified by the X and Y parameters. The Z parameter may be used tocapture values for many different types of quantities, as previouslydescribed. In one example relevant to the oil and gas industry, the Zparameter may be used to record values associated with sub-surfaceformation thickness. Such Z parameter values may be represented, forexample, by annotating a particular X, Y point with a particularthickness value. In this example the area of interest could include anoil field under consideration for exploration. The dimensions of thearea of interest in an oil exploration example may be on the order ofhundreds of meters to multiple kilometers.

Returning to the specific example shown in FIG. 2, input data 200includes a plurality of measured values each associated with a differentlocation within an area of interest. The X and Y parameter valuesdetermine where the points are placed on the map representative of thearea of interest. These map locations may indicate, for example, whereindividual measurements were taken. The numbers shown next to the pointson the input data map provide the value of the measured quantity at theparticular X, Y location. For example, continuing with the formationthickness example, a measured formation thickness value of 0 feet isassociated with location 210, a measured formation thickness value of 63feet is associated with location 220, and a measured formation thicknessvalue of 144 feet is associated with location 230.

Input data 200 provides a set of discrete locations were values for aparticular quantity are known. Input data 200, on its own, however,provides no indication of the values for the particular quantity atlocations within the area of interest other than at the known data pointlocations. Thus, in order to create a contour map filling in these gaps,an algorithm may be used to interpolate between the known data pointsand assign values to the quantity for points in the gaps between theknown data points.

Any suitable algorithm or mapping software may be used to generate agrid or contour map showing known and estimated values over an entirearea of interest. In some embodiments, a gridding algorithm may be used.Such gridding algorithms set a grid and grid size over the area ofinterest and, based on the known data points within the area ofinterest, calculate values for a particular quantity at each of thenodes of the grid.

In most cases, generating a contour map involves a step of selecting anarea of interest. The area of interest essentially corresponds to thearea to be mapped. This area will have a certain size determined by itsdimensions, boundaries, etc. For example, a biologist studying ants maywish to map an ant hill. In this case, the area of interest may havedimensions of only a few centimeters. A home owner planning a new gardenmay wish to map her back yard, and there, the area of interest may havedimensions on the order of a few tens of meters or maybe hundreds ofmeters. A cartographer wishing to produce a map of the entire UnitedStates would have an area of interest with dimensions on the order ofthousands of kilometers.

Another step in the generation of a contour map may include selection ofa grid and corresponding grid size. A grid may correspond to an internalcomputer representation of the surface being mapped. In someembodiments, the grid may be defined in terms of Cartesian coordinates,but any other suitable grid definitions may be used. Two primary factorsmay influence the selected grid size. These include the size of thefeatures being mapped and degree of distribution of the input data.According to sample theory principles, the sample rate should be onehalf of the smallest feature to be mapped. Therefore, a biologistmapping an ant hill may select a grid size on the order of millimeters.The home owner mapping her back yard may select a grid size on the orderof meters or decimeters. The cartographer mapping the United States mayselect a grid size on the order of kilometers or tens of kilometers.

Data distribution may be another factor to consider when selecting agrid size for a mapping algorithm. In some embodiments, the selectedgrid size may be less than half the distance between the closest datapoints. Where a grid size is selected that is larger than one half thedistance between the closest points, the possibility would exist thatone or more data points could fall within a single grid cell and becomesmoothed. It should be noted that in view of the ever-increasingcomputing power of modern processors, these processors are betterequipped than older processors to handle calculations for large numbersof grid nodes. Thus, unlike processors of the past that could take hoursor days to complete the computations required for a small selected gridsize, modern processors can perform many thousands or millions ofcomputations in fractions of a second. Thus, to minimize the risk ofdata point clustering or aliasing the features to be mapped, it may beprudent to err on the side of selecting a smaller grid size.

Once the grid and its size parameters have been selected or assigned,the next step in generating a contour map of values may includedetermining and assigning values to each node in the grid. This processmay include interpolation and/or extrapolation between known datapoints. In general, at nodes that coincide with or are very close toknown data points, the values assigned to those nodes may be the same asor very close to the values of the known data points. Away from theknown data points, however, values must be assigned to the nodes throughinterpolation or extrapolation, for example. Many algorithms areavailable for performing this type of interpolation or extrapolation,and each may have certain advantages or disadvantages depending on therequirements of a particular application. For example, differentalgorithms may be based on different sets of assumptions regarding howthe input data should be interpolated or extrapolated. One commonfeature with these interpolation or extrapolation algorithms is that allmay be used to calculate and assign values to the grid nodes away fromthe known input data points.

After assigning values to the grid nodes, the grid values may becontoured, and an output map may be generated. This output map may beshown on a display screen (e.g., a screen associated with a computermonitor, television, tablet computer, smart phone, cell phone, etc.),printed on paper or other media, stored in memory, etc. Alternatively,the grid may be used directly without conversion to contours for displayas a three-dimensional surface, color coded surface, shaded reliefsurface, etc. The grid may also be used as input for furthercalculations or processing.

Various types of algorithms may be used to determine and assign valuesto the nodes on the grid. Broadly speaking, such algorithms may bedivided into two broad classes: local interpolation algorithms andglobal extrapolation algorithms. In general, local interpolationalgorithms may focus on a localized collection of data points andinterpolate values between them. In most or even all cases, thecalculated value for a particular node on the grid will not exceed thevalues of the surrounding input data. Some examples of localinterpolation algorithms include triangulation, natural neighbors,moving average, inverse distance, kriging, and parabolic fitting, andcollated co-kriging, among others.

In general, global extrapolation algorithms tend to examine theavailable data and attempt to provide a global solution, most commonlythrough progressive refinement. In global extrapolation algorithms, itis not uncommon for values assigned to grid nodes to exceed input datavalues. Some examples of global extrapolation algorithms include cubicB-Spline function, minimum curvature, full tension, convergent gridding,and cos expansion, flex gridding, and gradient projection, among others.

FIG. 3 provides an example of a contour map 300 that was generated basedon input data 200. In this example, a grid and grid size were assigned,and the nodes on the grid were populated with values using a krigingalgorithm. Input parameters to the kriging algorithm included asemi-major axis, a semi-minor axis, and an azimuth value. For thecontour map 300 shown in FIG. 3, the parameter values selected were, asfollows: a semi-major axis of 3577; a semi-minor axis of 2322; and anazimuth value of −27. Units have been omitted as the mapping techniqueis applicable for any selected units.

Based on the known data input values 200, which in this examplerepresent formation thickness values within an area of interest, thekriging algorithm, and the specified parameter values for the krigingalgorithm, data values were calculated for each node of the grid. Thesecalculated values provide the basis for contour map 300. Each of thecontour lines on map 300 indicates those locations within the area ofinterest where the formation thickness has a constant value. Thegradient of the formation thickness in a certain region of the area ofinterest can be determined by looking in a direction perpendicular tothe contour lines. The spacing of contour lines indicates the magnitudeof the gradient in the data (or how rapidly the formation thicknesschanges within a particular region). As shown on map 300, region 310corresponds to a valley in the area of a plurality of known data pointsall having a zero thickness. In contrast, region 320 shows an area ofgenerally concentric contour lines surround a know data point having athickness value of 471 feet. The relatively close spacing between thecontour lines in the area suggests that the thickness in this region hasa local maximum and falls off fairly rapidly to lower values.

Contour map 300 may provide useful information regarding the potentialvalues associated with a quantity of interest away from the known datapoints. More information is needed, however, to provide additionalinformation regarding probabilities associated with the values of thequantity over the area of interest.

To generate probability maps, the presently disclosed systems may makeuse of stochastic or Monte Carlo techniques. Specifically, rather thancalculating only one contour map, such as contour map 300, based upon aunique set of input parameters to the gridding algorithm, the presentlydisclosed probability map generating systems may be configured to varythe input parameters and generate a contour map for each variation ofthe input parameters to the gridding algorithm. In this way, theprobability map generating systems can generate a statisticallysignificant number of contour maps (e.g., 50, 100, 200, or more) fromwhich a statistically robust probability map may be generated.

The input parameters to the gridding algorithm can be varied accordingto any suitable stochastic or Monte Carlo based process. In someembodiments, the input parameters may be randomly varied by using arandom number generator, for example. The input parameters may also bevaried according to a predetermined probability function. A variation ofthe input parameters may involve variation of only a single parametervalue, a portion of the available parameter values, or all of theavailable parameter values. The process of iteratively modifying atleast one input parameter associated with the mapping algorithm maycontinue until any desired number of maps of values (contour map, rawdata, or otherwise) has been generated. Depending on the particulargridding algorithm used, the input parameters that can be varied mayinclude a radius of influence, anisotropy, azimuth, semi major and semiminor axis, and the sill and nugget in the case of kriging. Each contourmap generated as a result of a variation to the input parameters to thegridding algorithm represents one possible distribution of the values ofthe quantity of interest between the discrete, known data points.

FIG. 4 shows a contour map 400 generated by modifying the inputparameter values of the gridding algorithm used to generate map 300shown in FIG. 3. Specifically, rather than using a semi-major axis of3577; a semi-minor axis of 2322; and an azimuth value of −27 as input tothe gridding algorithm (i.e., the input parameter values used togenerate map 300), these input parameter values were modified togenerate map 400. In the case of map 400, a semi-major axis of 8838; asemi-minor axis of 1040; and an azimuth value of 46 were used. While theunderlying set of known data points remains unchanged, map 400 hassignificant differences as compared to map 300. As previously noted,this process can be repeated until any number of data sets or contourmaps have been generated.

FIG. 5 shows another contour map 500 generated by modifying the inputparameter values of the gridding algorithm. In the case of map 500, asemi-major axis of 8031; a semi-minor axis of 2779; and an azimuth valueof 86 were used.

As previously indicated, an important aspect of the presently disclosedembodiments is the use of stochastic or Monte Carlo techniques to varythe parameters of the gridding algorithms to obtain a statisticallysignificant sample of possible maps. Different gridding algorithms,however, may use different parameters depending on the particularestimation techniques employed by the gridding algorithm. Further,different gridding algorithm venders may implement the algorithmsdifferently and limit the extent to which the parameters may be varied.Finally, some gridding algorithms, such as triangulation and the naturalneighbor algorithms, may be less suitable than others for the type ofparameterization necessary in making multiple estimations.

Despite potential differences among the various gridding algorithms,many commonalities may exist. For example, the concept of search radiusand anisotropy may be applicable across multiple gridding algorithms.The moving average gridding algorithm, which is a relatively simplegridding algorithm, can be used to illustrate how modifying the searchradius and anisotropy can be used to generate multiple versions of a mapfrom the same input data.

To generate data maps, known data points may be used to populate thenodes of a grid that covers the area of interest. For each node on thegrid the gridding algorithm may look for those data points that fallwithin the search radius and then assign to that grid node the averageof those known data points. By varying the size of the search radius thenumber of data points that are averaged can be changed, the valuesassigned to the grid nodes can be changed, and, therefore, the finalgrid and resulting map may be changed.

Additional variation may be achieved by introducing anisotropy. A simplesearch radius implies a circle, but frequently the use of an ellipse mayyield better results. By defining an aspect ratio, or a semi major andsemi minor axis, the circle may be converted to an ellipse. An ellipsewith an aspect ratio of 0.5 would have a semi major axis twice as longas the semi minor axis. The ellipse may also be oriented north-south,east-west, or any other desired direction. By changing the size, aspectratio and orientation (or azimuth) of the ellipse, the data points thatare averaged may change. As a result, the values of the grid nodes maychange and, therefore, the grid and final map may be changed. In thisway, iterative variation of the input parameters can lead to multiple,different maps being generated based on the same input data.

Various types of parameters can be varied depending on the particulargridding algorithms used. For example, search radius and anisotropy canbe used with most local interpolation algorithms. The inverse distancealgorithm has a decline rate parameter that may be varied. The krigingalgorithm allows for variation in the “sill and nugget” parameters.Regarding global extrapolation methods, most, if not all, allow forvariation in the anisotropy, as well as other parameters unique to thespecific algorithms. For example, in the minimum curvature algorithm,the curvature constraint may be relaxed, while in the full tensionalgorithm, the tension constraint may be relaxed.

All of the above noted algorithms generate grids which can then bedisplayed as contour maps (either paper or computer displayed), colorgraded displays, or three dimensional surfaces in computer graphics.These grids may also be output to ascii or binary files for import,display, and/or manipulation by other programs. In some embodiments thegenerated grids may be produced to comply with certain industry standardformats, such as CPS-3, EarthVision, Irap (ascii) and Irap (Binary),Petrel and Zmap+, among others.

As a further note regarding the stochastic processes associated with thedisclosed embodiments, almost all programming languages include one ormore random number generators. In the simplest form, the random numbergenerator can be used to generate numbers between two specifiedend-members. As noted previously, one of the most common parameters thatcan be varied, and perhaps the best way to implement stochasticvariation, is the use of anisotropy. One implementation of anisotropyuses semi major axis, semi-minor-axis, and azimuth. Using this as anexample, reasonable ranges for these parameters (depending on the sizeof the area of interest and data distribution) might be between 1000 mand 10,000 meters for the axis and 0 to 180 degrees for the azimuth. Therandom number generator can then be set to output numbers between thenoted end-members, and those numbers can then be used as variants to theinput gridding parameters.

Another approach may be to constrain the random number generator by aprobability function or histogram. Using the semi-major/semi-minor axisexample above, the lengths of these axes could reasonably vary between1000 m and 10,000 m, with a likely length of 4,500 m. If the p99 is at1000 m and the P01 is at 10,000 m, the distribution can be described asa normal or Gaussian probability distribution. This probability functioncan then be replaced by a histogram where the number of classes in thehistogram may be based on the number of iterations planned (or thenumber of times the maps will be generated). Each time the system goesthrough an iteration, the histogram may be interrogated to determine theclass to which the number produced by the random number generatorbelongs. If the number generator produces a number that belongs to aclass in the histogram that has already been filled, the number may berejected, and a new number may be output. In this manner, new numbersmay be generated for the gridding algorithm until the histogram isfilled.

While the processes described above for generating data sets and/or datamaps focused on varying the input parameters to gridding algorithms,other techniques may also be employed for providing data sets and/ordata maps. For example, as an alternative to, or in addition tovariation of the gridding algorithm input parameters, data sets and/ordata maps may also be generated by varying the data provided as input tothe gridding algorithm, among any other suitable techniques. Varying theinput data may include varying the values associated with the known datapoints used to populate the nodes of a grid covering an area ofinterest. One or more selected gridding algorithms may be run using anyor all of the varied input data sets in order to generate data setsand/or data maps corresponding to the area of interest.

The input data to the gridding algorithm can be varied according to anysuitable stochastic or Monte Carlo based process. The input data may berandomly varied by using a random number generator, for example. Theinput data may also be varied according to a predetermined probabilityfunction (e.g., gaussian, or any other suitable probability distributionfunction). A variation of the input data may involve variation of only asingle data value, a portion of the available data values, or all of theavailable data values. The process of iteratively modifying input dataprovided to a mapping algorithm may continue until any desired number ofmaps of values (contour map, raw data, or otherwise) has been generated.Such stochastic or Monte Carlo techniques to vary the input dataprovided to the gridding algorithms can be used to provide astatistically significant sample of possible maps from which a one ormore probability maps may be generated. Once a desired number of datasets or maps has been obtained, the process of producing a probabilitymap can continue. Any suitable technique for calculating probabilityinformation based on the generated data sets or maps may be used. Insome embodiments, the generated data sets or maps may be averagedtogether. Other techniques for calculating probability information basedon the generated data sets or maps may also be used alone or incombination with any other suitable techniques. For example, suchprobability information may be generated by determining a median, mean(average), mode, range, variance, deviation, standard deviation,skewness, kurtosis, etc. based on the generated data sets or maps.Alternatively, or additionally, the generated data sets or maps may beconverted to binary data sets or maps. This conversion may involvecomparing values in the generated data sets or maps to a predeterminedthreshold value. Values in the data set or map that equal or exceed thepredetermined threshold value, for example, may be assigned a new valueof one, and values that fall below the predetermined threshold value maybe assigned a value of zero. In this way, a binary map may be generatedfor each of the data sets or maps generated as part of the inputparameter variation process.

The predetermined threshold value can correspond to any suitable valuedepending on the requirements of a particular application. In someembodiments, the threshold value may correspond to a value for thequantity of interest identified as having a particular economicsignificance etc. For example, in the oil and gas exploration example,the threshold value may correspond to a particular formation thickness(e.g., 10 feet or other thickness of interest) used to determine whetherto establish a drilling operation. In the agricultural industry, thethreshold value may correspond to a particular rainfall amount.

FIG. 6 shows a binary map 600 generated based on map 300 of FIG. 3. Inthis example, the predetermined threshold value selected was 10 (e.g.,10 feet of thickness in the sub-surface formation). To generate map 600,the values assigned to the grid associated with map 300 were comparedwith respect to the predetermined threshold. For each node on the gridthat had a value of 10 or more, that value was replaced with a valueof 1. For each node on the grid that had a value less than ten, thatvalue was replaced with a value of 0. The resulting contour mapidentifies those regions, such as region 610, expected to have aformation thickness equal to or greater than 10 feet. Map 600 alsoidentifies those regions, such as regions 620, expected to have aformation thickness less than 10 feet. As shown on map 600, each of theknown data points having a value of zero falls within one of the regionsexpected to have a formation thickness less than 10.

FIG. 7 and FIG. 8 provide binary maps 700 and 800, respectively. Map 700represents a binary map generated using map 400, shown in FIG. 4, and apredetermined threshold value of 10. Map 800 represents a binary mapgenerated using map 600, shown in FIG. 5, and a predetermined thresholdvalue of 10.

Probability maps can be generated based on any number of binary grids,such those for maps 600, 700, and 800. In some embodiments, valuesassociated with corresponding nodes of 10, 50, 100, 200 or more binarygrids may be averaged to provide a probability grid. From thisprobability grid a probability contour map can be generated to show theprobability that any point away from a known data point has a valueabove the predetermined threshold value.

FIG. 9 shows a probability contour map 900 generated by averagingtogether binary maps, including binary maps 600, 700, and 800, amongmany others. In the example shown in FIG. 9, map 900 shows theprobability for all points over an area of interest that a sub-surfaceformation has a thickness of 10 feet or greater. The probability data isrepresented using contour lines. For example, contour line 910represents locations within the area of interest where there is acalculated 0% probability that the formation thickness is greater than10 feet. Contour line 920 represents locations within the area ofinterest where there is a calculated 50% probability that the formationthickness is greater than 10 feet, and contour line 930 representslocations within the area of interest where there is a calculated 100%probability that the formation thickness is greater than 10 feet. Allgrid values between known data points will vary between 1.0 and 0.0 (or100% and 0%).

In addition to the probability map shown in FIG. 9, which mapsprobabilities from 0 to 1.0, many other types of probability maps may begenerated consistent with the disclosed embodiments. For example, insome embodiments, probability maps may be generated based on discretedata points that represent the values of an attribute occurringcontinuously across a surface. The values of that attribute may beunknown between the selected discrete data points and values for thedata points range between 0 and 100. There may be an interest ingenerating a pX grid or map (e.g, a p90 grid or map that shows wherethere is a 90% probability that actual values will exceed those mappedand a 0.1 or 10% probability that actual values will be less than thosemapped.

To generate the probability map in this example, a gridding algorithmmay be selected that will interpolate between known data points andallow for modification of gridding parameters. Examples of such griddingalgorithms include kriging and minimum curvature, among others, asdiscussed above. A statistically significant number of grids(e.g., >100) may then be generated using stochastic or Monte-Carlotechniques to vary the gridding parameters either randomly or accordingto a probability function. Parameters that may be varied include radiusof influence, anisotropy, azimuth, semi major and semi minor axis, andin the case of kriging the sill and nugget. Each resulting maprepresents one possible distribution of the attribute between discretedata points. Each of the maps generated (or at least a subset of themaps generated) may be averaged. The resulting grid and contour map willshow the mean or P50 map (assuming a normal distribution). The P50 mapis one where for any point between known data points, there is a 50%probability that actual values will exceed those mapped and a 50%probability that actual values will be less than those mapped. Based onthe maps generated by varying the input parameters of the griddingalgorithm, a standard deviation map can be generated and multiplied by1.6. If this standard deviation map is subtracted from the P50 map, theresulting map is a P90 map in which where these is a 90% probabilitythat actual values will exceed those mapped and a 10% probability thatactual values will be less than those mapped.

Still other examples exist for generating probability maps in accordancewith the disclosed embodiments. For example, there may be an interest ingenerating a map that shows a P50 or mean distribution of data that arenot discrete, but have a probability distribution associated with them.The probability distribution may be due to errors in measurement orbecause the data represent averages (i.e. average rain fall, averageage, etc.). A probability distribution may be assigned to each datapoint in a particular set of data points that can be mapped. Theprobability distribution may be the same for each data point or may bedifferent. A statistically significant number of data sets may begenerated based on the assigned probability function for each of thedata points and by using a gridding algorithm and stochastically variedinput parameters. Averaging the grids or maps generated will result in amap that represents an average or P50 probability map (assuming a normaldistribution).

Once the probability maps have been generated, they may be subjected toa variety of post processing techniques. Many gridding algorithms mayproduce artifacts that result is maps that have “rough” looking contoursand/or spikes. Therefore, in some embodiments, the probability maps maybe subjected to processes for de-spiking and smoothing. Other commonpost processing tools may include dip and azimuth, which provideinformation on the rate of change and the direction of change.

An important aspect in generating probability maps is to have astatistically significant number of valid maps that can be used forstatistical analysis. The implicit assumption is that varying theparameters of the gridding algorithm between scientifically reasonableend members while holding the input data constant (or varying the inputdata between statistically reasonable end members) will provide astatistically significant number of valid maps.

As previously discussed, generation of a statistically significantnumber of maps may be accomplished using stochastic or Monte-Carlotechniques to vary the parameters of a gridding algorithm. The systemmay be initiated with a pre-set number of maps (e.g., 100, etc.). Eachtime a new map is generated, a random number generator may be used toprovide new input numbers for the gridding parameters. In this way, thesystem will generate 100 different unique maps.

The presently disclosed probability map generating systems and methodsmay be applied in a multitude of industries and applications. Creditcard companies may use this type of tool to evaluate the probabilitythat customers in certain geographic regions will pay for purchases orthe risk that customers in other geographic regions will default onpayments. Banks share similar concerns regarding loans. Investors may beinterested in the probability that certain investments will beprofitable weighed against the risk of loss. Insurance companies analyzeprobabilities associated with life span, health costs, driver safety,risks of injury, etc. These industries and many others can use theprobability mapping techniques to generate and analyze data based on aset of known data points.

The oil and gas exploration industry may also benefit from the presentlydisclosed probability map generating systems and methods. In thisindustry, only about one in eight, or about 12.5% of all explorationwells are successful. Many programs have been developed to help manageexploration and drilling risk. These programs generally work in asimilar way by estimating probabilities associated with factors thataffect the accumulation of hydrocarbons, including but not limited tosource, reservoir, seal, and structure are input into the system. Theseprograms may use Bayesian and/or Monte-Carlo statistical techniques toestimate the probability of success or risk of failure.

Such systems, however, rely on input that can be qualitative, which canaffect the usefulness of the probability information generated from thisinput. Much of the qualitative input is derived from expert opinion.Therefore, the final probability or risk output from these systems maybe only as good as the experts' opinions. The presently disclosedsystems and methods provide a technique for quantifying some of theinput parameters used in generating probability maps. This approach mayyield probability data less susceptible to the quality of qualitativeopinions.

The disclosed embodiments may be used in many applications within theoil and gas industry. For example, wells may be drilled at mappedlocations indicating there is a 90% chance of encountering more than acertain thickness of oil-containing material (e.g., a sandstoneformation). Insurance companies can use the disclosed embodiments toanalyze the risk of flooding in certain localities based on soilpermeability, rainfall probabilities, and/or groundwater runoff data.The environmental industry can determine probabilities that land is safefor habitation based on soil samples analyzed for levels of certaincontaminants. These are just a few of many potential applications inwhich the disclosed embodiments may be employed. Meteorologists cancreate better and statistically valid average rainfall maps. Further,using the disclosed embodiments, maps of any statistical measure (e.g.,mean, median, mode, variance, deviation, standard deviation, skewedness,etc.) can be generated, and various test of statistical significance canbe conducted, including the generation of probability maps.

1.-32. (canceled)
 33. A computer readable storage medium having computer readable program code embodied in the medium for use by a processor-based system in generating a probability map, the computer readable storage medium comprising: program code configured to: receive a geo-spatially discrete input data set associated with a quantity to be mapped; generate a statistically significant number of maps of values for the quantity within an area of interest based on the geo-spatially discrete input data set, wherein generation of the statistically significant number of maps includes applying a processor-based mapping algorithm to generate an initial map of values for the quantity within an area of interest based on the received geo-spatially discrete input data set, using a random number generator to iteratively modify the geo-spatially discrete input data set, and for each iterative modification of the geo-spatially discrete input data set, applying the mapping algorithm to the modified geo-spatially discrete input data set in order to generate an additional map of values for the quantity within the area of interest; and generate a probability map associated with the quantity based on the statistically significant number of maps by operating on the statistically significant number of maps.
 34. The computer readable storage medium of claim 33, wherein the program code is further configured to operate on the statistically significant number of maps by converting the statistically significant number of maps to corresponding binary maps based upon a predetermined threshold value and averaging the binary maps.
 35. The computer readable storage medium of claim 33, wherein operating on the statistically significant number of maps includes determining one or more of a median, mean(average), mode, range, variance, deviation, standard deviation, skewness, or kurtosis based on the statistically significant number of maps.
 36. The computer readable storage medium of claim 33, wherein the quantity includes at least one of geographic, topographic, bathometric, geologic, geophysical, petrophysical, oceanographic, metrological, atmospheric, hydrologic, pedologic (soil), chemical, environmental, sociologic, economic, biologic, zoological, botanical, epidemiologic, political, ecologic, reservoir engineering or mining data.
 37. The computer readable storage medium of claim 33, wherein the processor-based algorithm includes a local interpolation algorithm.
 38. The computer readable storage medium of claim 37, wherein the local interpolation algorithm includes a calculation based on at least one of triangulation, natural neighbors, moving average, inverse distance, kriging, parabolic fitting, or collated co-kriging.
 39. The computer readable storage medium of claim 33, wherein the processor-based algorithm includes a global extrapolation algorithm.
 40. The computer readable storage medium of claim 39, wherein the global extrapolation algorithm includes a calculation based on at least one of a cubic b-spline function, minimum curvature, full tension, convergent gridding, cos expansion, flex gridding, or gradient projection.
 41. A method of generating a probability map, comprising: receiving a geo-spatially discrete input data set associated with a quantity to be mapped; generating a statistically significant number of maps of values for the quantity within an area of interest based on the geo-spatially discrete input data set, wherein generating the statistically significant number of maps includes applying a processor-based mapping algorithm to generate an initial map of values for the quantity within an area of interest based on the received geo-spatially discrete input data set, using a random number generator to iteratively modify the geo-spatially discrete input data set, and for each iterative modification of the geo-spatially discrete input data set, applying the mapping algorithm to the modified geo-spatially discrete input data set in order to generate an additional map of values for the quantity within the area of interest; and generating a probability map associated with the quantity based on the statistically significant number of maps by operating on the statistically significant number of maps.
 42. The method of claim 41, wherein operating on the statistically significant number of maps includes: converting the statistically significant number of maps to corresponding binary maps based upon a predetermined threshold value; and averaging the binary maps.
 43. The method of claim 41, wherein operating on the statistically significant number of maps includes determining one or more of a median, mean (average), mode, range, variance, deviation, standard deviation, skewness, or kurtosis based on the statistically significant number of maps.
 44. The method of claim 41, wherein the quantity includes at least one of geographic, topographic, bathometric, geologic, geophysical, petrophysical, oceanographic, metrological, atmospheric, hydrologic, pedologic (soil), chemical, environmental, sociologic, economic, biologic, zoological, botanical, epidemiologic, political, ecologic, reservoir engineering or mining data.
 45. The method of claim 41, wherein the processor-based algorithm includes a local interpolation algorithm.
 46. The method of claim 45, wherein the local interpolation algorithm includes a calculation based on at least one of triangulation, natural neighbors, moving average, inverse distance, kriging, parabolic fitting, or collated co-kriging.
 47. The method of claim 41, wherein the processor-based algorithm includes a global extrapolation algorithm.
 48. The method of claim 47, wherein the global extrapolation algorithm includes a calculation based on at least one of a cubic b-spline function, minimum curvature, full tension, convergent gridding, cos expansion, flex gridding, or gradient projection. 